# LOGIC questions from "getting into oxbridge guide"

Ok people, these are some of the logic questions from the "getting into oxbridge for social sciences" guide which i need help with. There are quite a few so what i am going to do is post them individually then we can discuss solutions before posting the nest question. For some of them, i'm not even sure if there is a "CORRECT" answer! Anyway here goes with the first:

You are thinking of buying a second-hand car. You are prepared to pay £5000 for a good car, but only £1000 for a bad car. You do not know where the car which you are buying is in good or bad condition. However you believe that a quarter of the cars on the road are good and three quarters are bad.
(a) What is the expected value of the car to you?
(b) How much would you offer for the car? (no right or wrong answer so justify reasoning for answer)
(c) You know that the seller of a good car will only sell for a minimum of £4000, while a seller of a bad car will sell for a minimum of £500. What would you now offer for the car? (assume there are laws which make all bids binding, so they cannot be cahnged once an offer is accepted)
(d) How might the seller of the second hand car convince the buyer of the high quality?

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I'm really curious as to what this guide is... I never saw anything like this (Oxford PPE).

Anyway, this is just my initial reaction and I haven't thought hard, but...

a) £2k ([5*1+1*3]/2)

b) Probably about £500. You don't know whether you'll get a good or bad car, so you assume it might be bad, as you're unwilling to pay over the odds.

c) Still £500

I can think about it harder if you really want but I suspect those are the answers or something nearby.
You have not used the fact the you consider a quarter of the cars on the road to be good and three quarters to be bad. Do you think that this is irrelevant to confuse? I used teh information in part (a) as follows:

good price is £5000. a quarter of £5000 is £1250
bad price is £1000. Three quarters of £1000 is £750

£1250+£750=£2000

8 Lucky number
You have not used the fact the you consider a quarter of the cars on the road to be good and three quarters to be bad. Do you think that this is irrelevant to confuse? I used teh information in part (a) as follows:

good price is £5000. a quarter of £5000 is £1250
bad price is £1000. Three quarters of £1000 is £750

£1250+£750=£2000

It's basically the same method, just changing where you divide by 4.

The thing about the 1/4 of the cars being good is you don't know when they are. If you offer £500 to a bad car on offer you'd get it, though if you offer £500 to a good car you wouldn't. However, if you offer £4k you'd get either a good or a bad car, and probably a bad one. So it's not worth taking the risk.
Ok seeing as your a PPE'ist try this one from an economics interview at cambridge.

A man pay for his holiday on a desert island by cheque. The man has an excellent credit rating and so instead of cashing the cheque, the holtelier uses it to pay his supplier. The supplier uses the cheque to pay his supplier and so on forever. The question is, who pays for the mans holiday?
8 Lucky number
Ok seeing as your a PPE'ist try this one from an economics interview at cambridge.

A man pay for his holiday on a desert island by cheque. The man has an excellent credit rating and so instead of cashing the cheque, the holtelier uses it to pay his supplier. The supplier uses the cheque to pay his supplier and so on forever. The question is, who pays for the mans holiday?

Well, the man pays for his own holiday using the cheque. The hotelier wouldn't be allowed to use the cheque to pay someone else because it's addressed to him, so the question doesn't make sense.
(the man? )
8 Lucky number
Ok people, these are some of the logic questions from the "getting into oxbridge for social sciences" guide which i need help with. There are quite a few so what i am going to do is post them individually then we can discuss solutions before posting the nest question. For some of them, i'm not even sure if there is a "CORRECT" answer! Anyway here goes with the first:

You are thinking of buying a second-hand car. You are prepared to pay £5000 for a good car, but only £1000 for a bad car. You do not know where the car which you are buying is in good or bad condition. However you believe that a quarter of the cars on the road are good and three quarters are bad.
(a) What is the expected value of the car to you?
(b) How much would you offer for the car? (no right or wrong answer so justify reasoning for answer)
(c) You know that the seller of a good car will only sell for a minimum of £4000, while a seller of a bad car will sell for a minimum of £500. What would you now offer for the car? (assume there are laws which make all bids binding, so they cannot be cahnged once an offer is accepted)
(d) How might the seller of the second hand car convince the buyer of the high quality?

Havn't really thought about these but surely if the car is much more likely to be 'bad' then you would expect its value to be £1000 (with a 25% chance that its value is five times that).

I remember another question I read somewhere in an oxbridge interview. It said 'how would you find the height of a building using only a barometer?'. Answers included dropping the barometer from the top of the building and timing how long it took to hit the ground (and using constant accelaration equations) and finding the caretaker of the building and offering him the barometer if he told you the height of the building.
That's a good question
Ralfskini
I remember another question I read somewhere in an oxbridge interview. It said 'how would you find the height of a building using only a barometer?'. Answers included dropping the barometer from the top of the building and timing how long it took to hit the ground (and using constant accelaration equations) and finding the caretaker of the building and offering him the barometer if he told you the height of the building.

We discussed that in a Physics lesson. If you're only allowed to use a barometer, then presumably a stopwatch and a caretaker can't be used...

I think the boring "use the barometer to measure air pressure on the top and bottom of the building like you're supposed to" is the way to do it.
Squishy
Well, the man pays for his own holiday using the cheque. The hotelier wouldn't be allowed to use the cheque to pay someone else because it's addressed to him, so the question doesn't make sense.

If the cheque is not marked "Account Payee" anyone can bank it. Most chequebooks are Account Payee - for security, but it's not a feature of cheques in general; I have one which isn't "a/c payee" - though if I want it to be, I just scrawl the words on
amex
If the cheque is not marked "Account Payee" anyone can bank it. Most chequebooks are Account Payee - for security, but it's not a feature of cheques in general; I have one which isn't "a/c payee" - though if I want it to be, I just scrawl the words on

Yes, I have seen those...but I certainly wouldn't accept someone else's cheque as payment for something. But in the end, the man still pays (or owes the money) for the holiday...but if the cheque is never cashed, then that's a different story.
Squishy
We discussed that in a Physics lesson. If you're only allowed to use a barometer, then presumably a stopwatch and a caretaker can't be used...

I think the boring "use the barometer to measure air pressure on the top and bottom of the building like you're supposed to" is the way to do it.

Well if the question was estimate (as I'm sure it probably was) then you could use the dropping the barometer from the building method but you'd get a really crap estimate (probably no worse than the air pressure one as the buildig is probably not going to be high enough for there to be a significant diffrerence). Anyway, I would proceed by smashing the barometer into loads of pieces then *trying* to count how long it takes to fall and conduct numerous repeats with my many 'bits of broken barometer'.
Ralfskini
I remember another question I read somewhere in an oxbridge interview. It said 'how would you find the height of a building using only a barometer?'. Answers included dropping the barometer from the top of the building and timing how long it took to hit the ground (and using constant accelaration equations) and finding the caretaker of the building and offering him the barometer if he told you the height of the building.

I'd drop it and count. Air pressure, Pah! Tutors admire courage.
Surely the expected value of the car is £1000 as it is most likely to be bad, and therefore worth £1000?
BazTheMoney
I'd drop it and count. Air pressure, Pah! Tutors admire courage.

good man! Great minds think alike.
tomcoolinguk
Surely the expected value of the car is £1000 as it is most likely to be bad, and therefore worth £1000?

That's exactly what I said.
Ralfskini
Well if the question was estimate (as I'm sure it probably was) then you could use the dropping the barometer from the building method but you'd get a really crap estimate (probably no worse than the air pressure one as the buildig is probably not going to be high enough for there to be a significant diffrerence). Anyway, I would proceed by smashing the barometer into loads of pieces then *trying* to count how long it takes to fall and conduct numerous repeats with my many 'bits of broken barometer'.

Yeah, whatever way you do it, you probably won't get the right answer. Personally, I'd just keep the barometer and guess the building's height. Who cares if it's wrong?

As for the courage in interviews thing...OK, some people are brave, and I do admire people who will defend what they believe even if not many people agree with them, but I really think interviews should be about finding out how far people can think without any preparation. It's funny to hear about stories like the Philosophy applicant who supposedly wrote "No" to a question saying, "Is this question sensible?" and left, but how much of his intellect do you really see in that answer? He could just be some smartass who's not particularly hard-working or bright, and you wouldn't want him to come to your college just because he gave you a laugh.
I do think the first part is a right or wrong answer question; it is made clear that the car must be worth £1000 or £5000! As three quarters of cars cost £1000 this must be most common. Can't believe so many people have been tricked... tee hee. I feel a bit better about myself
Is it just me or does this question not really seem that challenging? For (d) is there in a sense the fact that the only way you could be convinced of the car's quality is if you examine it... the seller could refuse to budge from £4k but this is surely inconclusive- he could just be trying to get an unfair price.

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